4. Breakdowns on a certain stretch of motorway were recorded each day for 80 consecutive days. The results are summarised in the table below.
| 0 | 1 | 2 | \(> 2\) |
| Frequency | 38 | 32 | 10 | 0 |
It is suggested that the number of breakdowns per day can be modelled by a Poisson distribution.
Using a \(5 \%\) level of significance, test whether or not the Poisson distribution is a suitable model for these data. State your hypotheses clearly.
(13 marks)